Recently a state-specific multireference perturbation theory (SSMRPT) with an improved virtual orbitals complete active space configuration interaction (IVO-CASCI) reference function has been proposed for treating electronic structures of radicals such as methylene, m-benzyne, pyridyne, and pyridynium cation. This new development in MRPT, termed as IVO-SSMRPT, ensures that it is able to describe the structure of radicaloids with reasonable accuracy even with small reference spaces. IVO-SSMRPT is also capable of predicting the correct ordering of the lowest singlet triplet gaps. Investigation of the first three electronic states of the oxygen molecule has also been used for rating our method. The agreement of our estimates with the available far more expensive benchmark state-of-the-art ab initio calculations is creditable. The IVO-SSMRPT method provides an effective avenue with manageable cost/accuracy ratio for accurately dealing with radicaloid systems possessing varying degrees of quasidegeneracy.